Gas Supersaturation Thresholds for Spontaneous Cavitation in Water with Gas Equilibration Pressures up to 570 Atm1 Wayne A

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Gas Supersaturation Thresholds for Spontaneous Cavitation in Water with Gas Equilibration Pressures up to 570 atm1 Wayne A. Gerth and Edvard A. Hemmingsen *

Physiological Research Laboratory Scripps Institution of Oceanography University of California, San Diego La Jolla, California 92093

(Z. Naturforsch. 31a, 1711-1716 [1976] ; received October 5, 1976)

Supersaturations for the onset of cavitation in water were determined for various gases. At ambient pressure, the threshold supersaturations (in atm) required for profuse cavitation to initiate both in bulk water and at the glass-water interface were CH4, 120; Ar, 160; N2, 190; He, 360. Exposure of the water and its containing surfaces to hydrostatic pressures up to 1100 atm prior to equilibration with gas had no detectable effect on these threshold values. This indicates that pre- formed gas nuclei are not significantly involved. Cavitation at the glass-water interface was investi- gated for CH4, Ar and N, saturations up to 570 atm. For 320 atm saturations, the threshold supersaturation was about one-half that for decompression directly to ambient pressure, and for 550 atm it was about one-third. These results indicate that the dissolved gas concentration is a critical factor limiting the spontaneous nucleation of bubbles in gas supersaturated liquids.

Introduction thereby forcing the resolution of such dissolvable nuclei 4. Water that contains large gas supersaturations The results reported here bear directly upon the can remain stable with the absence of cavitation 2' 3. understanding of the gas supersaturated metastable However, as the gas supersaturation in the water is condition in pure liquids, the factors which limit it, increased, the system eventually fails to tolerate the and the characteristics of its degeneration via the supersaturation and bursts profusely with the for- nucleation and growth of bubbles. These results also mation of bubbles. Hemmingsen 3 reported the lar- have implications for the understanding of the for- gest observed gas supersaturation stabilities of water mation of bubbles in organisms with gas super- and found that the minimum supersaturation re- saturated tissues, such as occurs in conjunction with quired for cavitation inception, in the apparent ab- decompression sickness in aviators and divers5'6 sence of pre-formed nuclei, varied substantially with and in tumors supersaturated with oxygen from in- different gases in solution. This threshold super- jection of hydrogen peroxide as an adjuvant to saturation generally increased with decreasing gas radiation therapy 7. solubility, suggesting that the total concentration of gas in solution is important in determining the gas supersaturation stability of liquids. Methods Our efforts to further characterize cavitation nucleation phenomena required examination of this The apparatus (Fig. 1) was designed to first hy- concentration effect in some detail. An experimental drostatically pressurize water, then to equilibrate a system was developed in which wide ranges of gas small portion under high gas pressure, and finally, to transfer it under pressure into an observation pressure could be used to vary the dissolved gas capillary where it could be observed with a binocu- concentrations, necessitating the minimization of lar microscope (15 x) during decompression. All interference by foreign gas nuclei whose persistence chambers and tubing were made of stainless steel. in the water and on container surfaces could vary as Chamber A contained a 2.5 cm thick quartz viewing a function of pressure. This was accomplished by port and a plexiglass lighting port. The pyrex obser- applying large hydrostatic pressures to the water and vation capillary (0.011cm I.D.) was placed inside the container surfaces prior to solution of the gas, this chamber to enable high pressurization of the water and its container surfaces. The capillary had a volume of 0.07 ml and was connected with a * Reprint requests to Dr. Edvard A. Hemmingsen, A-004 plastic sleeve to a steel tube (0.025 cm I.D.) pro- Physiological Research Laboratory, Scripps Institution of Oceanography, La Jolla, CA 92093, USA. truding into the chamber. The pyrex sample bowl 1712 \V. A. Gerth et al. • Gas Supersaturation Thresholds for Spontaneous Cavitation 1712

Screw sample bowl was equilibrated with gas at the desired pressure for at least one hour while being stirred at To Gas Cylinder Capillary 60 rpm with a small Teflon-coated stirring bar. After equilibration, the water was slowly forced into the capillary from the sample bowl by slightly c. loosening the inner screw which maintained the seal kxbvM over the capillary venting device until the sample bowl was nearly emptied. The gas remaining in To Hydrauli* chamber A was replaced isobarically with water -Hp-' PPumu p from chamber B to prevent fogging during decom- Ven, pression. Chamber A was decompressed immediately thereafter while visually observing the capillary for the appearance of bubbles. In one series of experiments, the chamber was rapidly (2 — 3 seconds) decompressed directly to ambient pressure. In sub- sequent experiments, gradual decompressions were used and the pressures at which bubbles were first visible in the capillary were noted. The supersaturation tension was then defined as the difference between the equilibration pressure and the latter decompression pressure. Cavitation was characterized as follows: no cavitation — no bubbles formed in the capillary within approximately 2 minutes of decompression; light cavitation — relatively few (1 — 20) bubbles formed, Fig. 1. Schematic diagram of apparatus with enlarged il- leaving most of the water in the capillary bubble lustration of Chamber A showing arrangement of observation free; massive cavitation — bubbles formed effer- capillary, venting device, and sample bowl. vescently. Moderate cavitation characterizes those intermediate cases in which many bubbles formed throughout the capillary, but in which the cavitation had a volume of 1.5 ml and was secured in the was judged to fall short of effervescence. chamber with a plexiglass retainer. The capillary venting device on top of the chamber had a Viton rubber seal retained by a piston and screw assembly. Results Chamber B, with a movable "0" ring sealed plexi- The cavitation behavior of hydrostatically pre- glass piston, could be filled below the piston with pressurized water, gas supersaturated by decom- water, gas equilibrated with only atmospheric pres- pression directly to ambient pressure, is shown in sure. Figure 2. Also shown are experiments in which no Each of the gases used: methane, argon, nitrogen special hydrostatic pre-treatment of the water was and helium; had a purity greater than 99.9%. Com- used. Absence of cavitation with supersaturation mercial bottled distilled water was used without further treatment. Experiments were conducted at tensions of 100 atm or more was possible with each room temperature which usually ranged from 19 C of the gases. The greatest supersaturation tension to 21 C. The capillary was cleaned in concentrated with absence of cavitation was obtained with He at sodium dichromate — sulfuric acid solution and 320 atm. With increasing gas supersaturations, bub- rinsed with distilled water before installation in the bles began to form in increasing numbers. The onset chamber and periodically during the investigation. of cavitation occurred at different supersaturations Capillaries found to have obvious flaws adversely for each of the gases. Light to moderate cavitation affecting the gas supersaturation stability of the always appeared to initiate at or near the glass- water were replaced. water interface. Massive cavitation, however, was Chamber A was filled completely with water with caused by widespread fracturing of the water both the hydraulic pump at the start of each experiment. at the glass-water interface and uniformly in the Hydrostatic pressure from 935 atm to 1100 atm was then applied for a period of at least 15 minutes, bulk water, and was never observed below a certain after which water was slowly forced out the bottom supersaturation tension which was specific for each inlet by gas pressure. The water retained in the gas. The supersaturation threshold for cavitation in \V. A. Gerth et al. • Gas Supersaturation Thresholds for Spontaneous Cavitation 1713

bulk water, i. e. the bulk threshold, required in ex- i. e., the interface threshold, is shown as a function cess of ambient pressure was 120 atm for CH4, of gas equilibration pressure in Figure 3 A. When 160 atm for Ar, 190 atm for N2, and approxi- decompressed from high gas equilibration pressures, mately 360 atm for He. The bulk threshold for He the water tolerated lesser supersaturations before was less well defined than for the other gases due cavitating than when decompressed from lower gas to the rapid expansion of bubbles at the glass-water equilibration pressures. interface. Comparison with data obtained without In Fig. 3 B, the interface thresholds are nor- hydrostatic pre-pressurization of the water (also see malized, for each of the gases respectively, about Ref. 3) indicates that pre-pressurization had no no- their bulk threshold at ambient pressure. Each nor- ticeable effect on any cavitation character except for malized supersaturation (F) is defined as: the supersaturation required for inception of very light cavitation, which in only a few cases was slightly decreased. where Px = the bulk threshold at ambient pressure; Bubbles formed well before ambient pressure had n~Pt = the gas equilibration pressure expressed in been readied during decompression from pressures terms of Px; and P(. = the hydrostatic pressure at which cavitation was first observed to occur during greater than those required to produce the above , bulk thresholds. Using slower and often stepwise decompression from n P1. The normalized curves decompressions from these higher pressures, it was indicate that the relative stability of all the gas solu- found that bubbles forming at and adhering to the tions was affected similarly by increasing satura- glass-water interface were usually the first to ap- tions. At first, the interface threshold decreased pear; though often quite numerous (20 — 200), they rapidly with increasing equilibration pressures, and grew slowly in size. Upon continued decompression, then they tended to level off to a slower change at bubbles appeared and developed in the bulk water. higher pressures. For example, the interface thresholds, with decompressions from 320 atm, were nearly The minimum gas supersaturation tension re- half those with decompressions from pressures required for the onset of cavitation at the interface, quired to produce the bulk thresholds at ambient I i ÖÖ® <30(3 0 pressure, and with decompressions from 550 atm aaa OÜÖCM gas saturations, they had dropped to about a third. He a a a • • a a a • • • •aa aaa • I Even though the bulk thresholds were more diffi- cult to quantify due to interference of water move- ment and gas depletion from the expansion of bubbles at the interface, varying the gas equilibration pressure appeared to have a differing effect upon the aaai interface threshold relative to the corresponding effect upon the bulk threshold, depending upon the mit decompression rate. Thus, during slow gradual de- CH compressions, bubbles occurred first at the interface •Dan • o no cavitation at consistently lower supersaturations than those a.® light cavitation required for cavitation in bulk. In contrast, during a ® moderate cavitation very rapid decompressions, the appearance of these Ar O 9 9 « • • massive cavitation a aai interfacial bubbles was delayed enough for decom- • a aaai pression to proceed to the larger supersaturations J 50 100 150 200 250 300 350 400 450 required for nucleation in bulk water, which in these Gas Supersaturation Tension (ATM) cases, was observed to occur either concurrently Fig. 2. Cavitation behavior of water supersaturated with with or before the interfacial cavitation. various gases, decompressed to ambient pressure. The water was either hydrostatically pressurized to a minimum of 935 Discussion ATM for more than 15 minutes prior to equilibration with gas (squares), or was not pre-pressurized (circles). Tagged Cavitation inception in gas supersaturated liquids circles are representative data, reported in full elsewhere, obtained using a slightly different method 8. Each symbol may occur in the three different ways; inception (i) represents one experiment. by pre-formed gas nuclei stabilized either on par- 1714 \V. A. Gerth et al. • Gas Supersaturation Thresholds for Spontaneous Cavitation 1714

Fig. 3. A) Minimum gas 1501— Nitrogen Argon supersaturation tension required for cavitation ini- Methane tiating at the glass-water interface as a function of the gas equilibration pressure (re-Pt). Each point represents the lowest such supersaturation tension obtained from several experiments using a given gas equilibration pressure. B) Relation with gas equilibration pressure of the A above interface threshold supersaturations, normalized about the respective bulk cavitation threshold supersaturation tension at ambi- o 100 200 300 400 500 600 ent pressure (Pt) : CH4, Pi = 120 ATM; Ar, Pi = I.Or 160 ATM; N*, Pi = 190 ATM.

0.01~L_ 0 100 200 300 400 500 600 Gas Equilibration Pressure (ATM) tides suspended in the liquid4 8-10 or on container water, but decreased with increasing gas equilibra- surfaces8, (ii) by nuclei formed spontaneously in tion pressure. bulk liquid, involving only dissolved gas and the In some cases showing only very light cavitation, liquid n, and (iii) by nuclei formed spontaneouslv the contribution of pre-formed nuclei may have been at solid-liquid interfaces n~13. significant and indeed, they may have been respon- In the present experiments, cavitation was ini- sible for a few of the cases in which such light cavi- tiated predominantly by the latter two processes. tation occurred at supersaturations unusually low This is substantiated by several observations made with respect to that required to elicit massive cavita- here and in other related investigations 3 which are tion. Generally, however, it appears that the appli- inconsistent with the behavior expected for pre- cation of gas pressure induces sufficient hydrostatic formed gas nuclei. (I) The interface threshold su- pressure in the water to force nearly all pre-formed persaturations qualitatively paralleled the corre- nuclei into solution 3. Thus, though threshold super- sponding bulk threshold supersaturations; only saturations remain relatively unaffected by pre- moderate increases of supersaturation over those formed nuclei, the maximum supersaturation elicit- showing no cavitation were sufficient to elicit ing no cavitation may be sensitive to this type of a dense uniform distribution of bubbles throughout interference, as are some other types of cavitation the water volume and at the glass-water interface of processes. For example, in determinations of the the capillary. (II) Both interface and bulk thresh- tensile strength of liquids even a single nucleation olds were different for and characteristic of each gas. focus is sufficient to interrupt the cohesive conti- (Ill) Hydrostatic pre-pressurization of the water nuity of the stressed liquid 10; 14-1 had no effect on the bulk thresholds and only rarely Since our experimental technique only allowed affected the interface thresholds. (IV) The interface quantitative determination of the thresholds for thresholds were not constant, even for a given gas in cavitation at the glass-water interface, many of the \V. A. Gerth et al. • Gas Supersaturation Thresholds for Spontaneous Cavitation 1715 inferences made here apply strictly only to this imposes a major limitation on the nucleation process. type of spontaneous nucleation. However, inasmuch Another point which must be mentioned here is the as bulk water cavitation required only moderately unreasonable critical size requirement which appli- higher supersaturations, and in other respects did cation of the Laplace equation imposes on nuclei 3. not appear to dilfer substantially from the interface Rather, it appears that the total dissolved gas cavitation, some general conclusions may be reached concentration is an important factor limiting the about the nucleation process. nucleation process. The threshold supersaturations The observation that bubbles can occur sponta- generally are lower when the concentration of dis- neously in a given gas-liquid solution at different solved gas is higher. This applies to experiments supersaturation tensions (Fig. 3) raises a question where the gas concentration is varied in a given gas- about the adequacy of the Laplace equation for water solution and to experiments in different liq- estimating a critical size of the initial nuclei formed. uids with various solubilities of various gases. This equation, conventionally applied to descrip- tions of the nucleation process8'18'19 gives the However, for each gas, the decrease in the interface threshold tends to level off to a slower change equilibrium critical radius (r,.r) of a spherical bubble above which growth to macroscopic size with progressively greater saturations. This and the proceeds unabated, and below which collapse bade abrupt drop in supersaturation stability observed in into solution occurs. The minimum supersaturation water below 3.5 cC3, indicates that properties of tension (AP) in excess of any given hydrostatic the gas-liquid solution other than those related di- pressure, required by an incipient nucleus to reach rectly to gas concentration can also limit the mini- this critical size is given by AP = 2 o/r„, where mum threshold values. Thus, the present observation o = the gas-liquid surface tension. This relationship that bubbles usually first appear at the glass-water when applied to the present data requires that either interface must be related to interactions between the the surface tension or the critical radius, or both, gas and solvent liquid which are peculiar to the varied as a function of pressure. boundary layer immediately adjacent to the interface. For example, gas adsorption or kinetic inter- Several facts indicate that variation of the surface actions at the interface, or variations in water struc- tension cannot account for our observations. Even ture induced by proximity to the interface27' 28 or though the surface tension of water varies with in- a flux anisotropy induced by the interface upon creasing gas partial pressure at the gas-water inter- interfacial nuclei 21 may become significant. face 20, this variation over the ranges of gas pressures used here amounts to only a few percent, both The mechanism by which gas concentration affects with increasing gas partial pressure and between the nucleation process is not yet clear. Spontaneous different gases 20, whereas the observed reduction of nuclei have been suggested to arise from "holes" or the interface thresholds was, in each case, greater density dilations postulated to occur uniformly in than 60 percent. It is unlikely that the nucleation bulk liquid as a result of thermal fluctuations u' 22_25. event can be sensitive enough to these relatively Successful nucleation requires that some of these small changes in surface tension to cause such large nuclei reach and exceed some critical size ripidly reductions of the interface threshold values. Further- enough to overcome the tendency for collapse and more, such sensitivity would cause the threshold resolution. This may occur both by aggregation of curves for the various gases to diverge from each nuclei and accumulation of gas from solution into other with increasing gas saturations. This was the nuclei. Increasing gas concentrations may in- clearly not the case; the relative threshold super- crease the temporal stability of these subcritical saturations varied similarly with increasing equi- nuclei and/or their growth rates; each effect could libration pressures. Previous data also discount such augment the aggregation of such nuclei and facili- an extreme sensitivity to changes of surface tension; tate successful nucleation at lower supersaturation only minor variations of cavitation properties oc- tensions. Also, the solution of gases in water may curred in different liquids with wide ranges of sur- induce changes in the molecular structure of the face tension 3. Since neither the interface nor bulk water26 which could in turn cause the gas super- thresholds can be related to known variations of saturation stability to vary with dissolved gas con- surface tension, it is doubtful that this parameter centration. 1716 \V. A. Gerth et al. • Gas Supersaturation Thresholds for Spontaneous Cavitation 1716

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